{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5dcf4852",
   "metadata": {},
   "source": [
    "# 高等数学"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38a714b2",
   "metadata": {},
   "source": [
    "## 目录"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e6a2586",
   "metadata": {},
   "source": [
    "### 一、微积分基础"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3c26920",
   "metadata": {},
   "source": [
    "# 极限（1-70页）上"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38ac253a",
   "metadata": {},
   "source": [
    "### 极限知识点概述\n",
    "\n",
    "#### 1. 极限的基本概念\n",
    "\n",
    "- **定义**：极限是描述函数在某一点附近的行为或趋势的数学概念。当自变量趋近于某个值时，函数值的极限即为该函数在该点附近的趋势所逼近的常数（如果存在）。\n",
    "\n",
    "- **表示方法**：通常使用 $\\lim_{{x \\to a}} f(x) = L$ 来表示当 $x$ 趋近于 $a$ 时，函数 $f(x)$ 的极限为 $L$。\n",
    "\n",
    "#### 2. 极限的性质\n",
    "\n",
    "- **线性性质**：$\\lim_{{x \\to a}} (k \\cdot f(x) + b) = k \\cdot \\lim_{{x \\to a}} f(x) + b$，其中 $k$ 和 $b$ 是常数。\n",
    "\n",
    "- **乘积与商的极限**：若 $\\lim_{{x \\to a}} f(x) = L$ 且 $\\lim_{{x \\to a}} g(x) = M$，则 $\\lim_{{x \\to a}} (f(x) \\cdot g(x)) = L \\cdot M$（当 $M \\neq 0$ 时，$\\lim_{{x \\to a}} \\frac{f(x)}{g(x)} = \\frac{L}{M}$）。\n",
    "\n",
    "- **夹逼定理**（三明治定理）：若存在函数 $g(x) \\leq f(x) \\leq h(x)$，且 $\\lim_{{x \\to a}} g(x) = \\lim_{{x \\to a}} h(x) = L$，则 $\\lim_{{x \\to a}} f(x) = L$。\n",
    "\n",
    "#### 3. 常见的极限类型\n",
    "\n",
    "- **无穷大与无穷小**：$\\lim_{{x \\to a}} f(x) = \\infty$（或 $-\\infty$）表示当 $x$ 趋近于 $a$ 时，$f(x)$ 趋于正无穷（或负无穷）。$\\lim_{{x \\to a}} f(x) = 0$ 表示当 $x$ 趋近于 $a$ 时，$f(x)$ 趋于零。\n",
    "\n",
    "- **0/0型与∞/∞型不定式**：这类极限通常需要使用洛必达法则（L'Hôpital's rule）或其他技巧来求解。\n",
    "\n",
    "- **其他类型的不定式**：如0×∞型、∞-∞型等，可通过代数变换转化为0/0型或∞/∞型，再应用洛必达法则。\n",
    "\n",
    "#### 4. 洛必达法则\n",
    "\n",
    "- **定义**：在求解0/0型或∞/∞型不定式时，若满足一定条件（如函数在某点的导数存在且连续），则可通过求导数来简化极限的求解过程。\n",
    "\n",
    "- **应用**：$\\lim_{{x \\to a}} \\frac{f(x)}{g(x)} = \\lim_{{x \\to a}} \\frac{f'(x)}{g'(x)}$（在适用条件下）。\n",
    "\n",
    "#### 5. 极限的运算技巧\n",
    "\n",
    "- **因式分解**：通过因式分解消除分母或分子的零因子。\n",
    "\n",
    "- **有理化**：对于包含根号或分数的表达式，通过有理化消除根号或简化分数。\n",
    "\n",
    "- **泰勒展开**：对于复杂函数，可通过泰勒级数展开来近似求解极限。\n",
    "\n",
    "- **变量替换**：通过变量替换简化极限表达式。\n",
    "\n",
    "#### 6. 极限的存在性与唯一性\n",
    "\n",
    "- **存在性**：并非所有函数在所有点处都有极限。函数在某点处的极限存在需满足一定条件（如函数在该点附近的行为是稳定的）。\n",
    "\n",
    "- **唯一性**：若函数在某点处的极限存在，则该极限是唯一的。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a1b088de",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sympy as sp\n",
    "x = sp.symbols('x')\n",
    "f = sp.sin(x) / (sp.exp(x**2) - 1)\n",
    "p = sp.plot(f, (x, -2, 2), ylim=(-10, 10), show=False) \n",
    "p.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7077a8e1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7320508075688774\n"
     ]
    }
   ],
   "source": [
    "import sympy as sp\n",
    "f = lambda x: (3 + 3*x) / (3 + x)\n",
    "x1 = 1\n",
    "for i in range(1000):\n",
    "    x1 = f(x1)\n",
    "print(x1.evalf() if isinstance(x1, sp.Basic) else x1)  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7bbae141",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "5\n",
      "False\n"
     ]
    }
   ],
   "source": [
    "import sympy as sp\n",
    "x = sp.symbols('x')\n",
    "f1_expr = x**2 - 6\n",
    "f2 = lambda x: 2*x - 1\n",
    "limit_value = sp.limit(f1_expr, x, 3)  \n",
    "f2_value = f2(3)\n",
    "are_equal = limit_value == f2_value\n",
    "print(limit_value)  # 这将输出 3\n",
    "print(f2_value)     # 这将输出 5\n",
    "print(are_equal)    # 这将输出 False"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3005dc81",
   "metadata": {},
   "source": [
    "# 导数与微分（73-122页）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feadba9e",
   "metadata": {},
   "source": [
    "### 导数与微分知识点\n",
    "\n",
    "#### 一、导数的概念\n",
    "\n",
    "1. **定义**：\n",
    "   - 导数描述了函数值随自变量变化的快慢程度，即函数在某一点的切线斜率。\n",
    "   - 对于函数$y = f(x)$，其在$x_0$处的导数定义为：\n",
    "     \\[\n",
    "     f'(x_0) = \\lim_{{\\Delta x \\to 0}} \\frac{{f(x_0 + \\Delta x) - f(x_0)}}{{\\Delta x}}\n",
    "     \\]\n",
    "\n",
    "2. **几何意义**：\n",
    "   - 函数$y = f(x)$在点$x_0$处的导数$f'(x_0)$等于曲线$y = f(x)$在点$(x_0, f(x_0))$处切线的斜率。\n",
    "\n",
    "3. **物理意义**：\n",
    "   - 在许多物理问题中，导数表示了某种量的瞬时变化率，如速度、加速度等。\n",
    "\n",
    "#### 二、导数的计算\n",
    "\n",
    "1. **基本公式**：\n",
    "   - 常数的导数为0：$(C)' = 0$\n",
    "   - 幂函数的导数：$(x^n)' = nx^{n-1}$\n",
    "   - 指数函数的导数：$(e^x)' = e^x$\n",
    "   - 对数函数的导数：$(\\ln x)' = \\frac{1}{x}$\n",
    "   - 三角函数的导数：$(\\sin x)' = \\cos x$，$(\\cos x)' = -\\sin x$\n",
    "\n",
    "2. **运算法则**：\n",
    "   - 加法法则：$(u + v)' = u' + v'$\n",
    "   - 减法法则：$(u - v)' = u' - v'$\n",
    "   - 乘法法则：$(uv)' = u'v + uv'$\n",
    "   - 除法法则：$\\left(\\frac{u}{v}\\right)' = \\frac{u'v - uv'}{v^2}$（$v \\neq 0$）\n",
    "\n",
    "3. **链式法则**：\n",
    "   - 对于复合函数$y = f(g(x))$，其导数为：\n",
    "     \\[\n",
    "     \\frac{dy}{dx} = \\frac{dy}{du} \\cdot \\frac{du}{dx}\n",
    "     \\]\n",
    "\n",
    "#### 三、微分\n",
    "\n",
    "1. **定义**：\n",
    "   - 函数$y = f(x)$在$x_0$处的微分定义为：\n",
    "     \\[\n",
    "     dy = f'(x_0) \\Delta x\n",
    "     \\]\n",
    "   其中，$\\Delta x$是自变量$x$的增量，$dy$是函数值$y$的对应增量。\n",
    "\n",
    "2. **几何意义**：\n",
    "   - 微分表示了函数图像在一点附近的小变化量，即切线上的一段小线段。\n",
    "\n",
    "3. **计算**：\n",
    "   - 已知函数在某点的导数，即可通过微分公式计算该点附近的函数值变化量。\n",
    "\n",
    "4. **应用**：\n",
    "   - 微分在近似计算、误差分析、优化问题等方面有广泛应用。\n",
    "\n",
    "#### 四、高阶导数与高阶微分\n",
    "\n",
    "1. **高阶导数**：\n",
    "   - 对函数进行多次求导，得到的结果称为高阶导数。\n",
    "   - 如二阶导数：$f''(x) = (f'(x))'$\n",
    "\n",
    "2. **高阶微分**：\n",
    "   - 对函数进行多次微分，得到的结果称为高阶微分。\n",
    "   - 如二阶微分：$d^2y = f''(x) dx^2$\n",
    "\n",
    "#### 五、导数的应用\n",
    "\n",
    "1. **极值与最值**：\n",
    "   - 通过求导数并令其为0，可以找到函数的极值点。\n",
    "   - 结合二阶导数可以判断极值的类型（极大值或极小值）。\n",
    "\n",
    "2. **曲线的凹凸性与拐点**：\n",
    "   - 通过二阶导数可以判断曲线的凹凸性。\n",
    "   - 二阶导数变号的点即为拐点。\n",
    "\n",
    "3. **洛必达法则**：\n",
    "   - 用于求解某些类型的极限问题，特别是当分子和分母都趋于0或无穷大时的极限。\n",
    "\n",
    "4. **泰勒公式与近似**：\n",
    "   - 通过泰勒公式可以将函数在某点附近表示为多项式形式，从而进行近似计算。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9e681253",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-cos(1) + 2*sin(1)\n",
      "-cos(1) + 2*sin(1)\n"
     ]
    }
   ],
   "source": [
    "import sympy as sp\n",
    "x, t = sp.symbols('x t')\n",
    "f = sp.Piecewise((x**2 * sp.sin(1/x), x != 0), (0, x == 1))\n",
    "left_limit = sp.limit((f.subs(x, 1 + t) - f.subs(x, 1)) / t, t, 0, '-')\n",
    "right_limit = sp.limit((f.subs(x, 1 + t) - f.subs(x, 1)) / t, t, 0, '+')\n",
    "print(left_limit)  # 这将计算并输出左极限\n",
    "print(right_limit) # 这将计算并输出右极限"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "c9bb43a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2]\n",
      "[3/2]\n"
     ]
    }
   ],
   "source": [
    "import sympy as sp\n",
    "x = sp.symbols('x')\n",
    "expr = 2*x**3 - 9*x**2 + 12*x - 3\n",
    "f = sp.Lambda(x, expr)\n",
    "f1_expr = sp.diff(expr, x)\n",
    "f2_expr = sp.diff(expr, x, 2)\n",
    "f1 = sp.Lambda(x, f1_expr)\n",
    "f2 = sp.Lambda(x, f2_expr)\n",
    "r1 = list(sp.solveset(sp.Eq(f1_expr, 0), x))\n",
    "r2 = list(sp.solveset(sp.Eq(f2_expr, 0), x))\n",
    "print(r1)  # 一阶导数等于零的解\n",
    "print(r2)  # 二阶导数等于零的解"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59493361",
   "metadata": {},
   "source": [
    "# 积分（第184-270页）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bafb24d",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "### 积分概述\n",
    "\n",
    "- **定义**：积分是数学中用于求解函数在特定区间内累积效果（如面积、体积等）的一种方法。\n",
    "- **分类**：积分主要分为定积分和不定积分两种。\n",
    "  - **定积分**：指对一个函数在一个给定的区间内求积分，具有明确的积分上下限。\n",
    "  - **不定积分**：指对一个函数的积分不指定上下限，通常表示为一个函数族（原函数）。\n",
    "\n",
    "### 定积分\n",
    "\n",
    "- **符号**：$\\int_a^b f(x) \\, dx$，其中$a$和$b$是积分上下限，$f(x)$是被积函数。\n",
    "- **性质**：\n",
    "  - 线性性：$\\int_a^b (k_1f(x) + k_2g(x)) \\, dx = k_1\\int_a^b f(x) \\, dx + k_2\\int_a^b g(x) \\, dx$。\n",
    "  - 可积性：若$f(x)$和$g(x)$在$[a, b]$上可积，则它们的乘积$f(x)g(x)$也在$[a, b]$上可积。\n",
    "  - 保号性和保序性：若积分下限小于积分上限，且被积函数大于等于0，则积分大于等于0。\n",
    "  - 区间的可加性：若积分在各区间上可积，则可以在积分上下限中间插入任意点，构成的各区间上定积分和等于原积分。\n",
    "- **计算方法**：\n",
    "  - 基本积分公式：如$\\int x^n \\, dx = \\frac{1}{n+1}x^{n+1} + C$（$n \\neq -1$）。\n",
    "  - 换元积分法：通过变量替换简化积分。\n",
    "  - 分部积分法：适用于两个函数的乘积的积分。\n",
    "\n",
    "### 不定积分\n",
    "\n",
    "- **符号**：$\\int f(x) \\, dx$，表示$f(x)$的不定积分或原函数。\n",
    "- **性质**：\n",
    "  - 不定积分是定积分的逆运算，但不定积分的结果是一个函数族，而定积分的结果是一个数值。\n",
    "- **计算方法**：\n",
    "  - 基本积分公式。\n",
    "  - 换元积分法。\n",
    "  - 分部积分法。\n",
    "  - 有理函数的积分：部分分式法。\n",
    "  - 三角函数的积分：利用三角恒等式和换元法。\n",
    "  - 特殊函数的积分：如指数函数、对数函数等，有特定的积分公式。\n",
    "\n",
    "### 积分的应用\n",
    "\n",
    "- **面积计算**：通过定积分可以计算平面图形的面积。\n",
    "- **体积计算**：通过二重积分或三重积分可以计算立体图形的体积。\n",
    "- **物理应用**：积分在物理学中有广泛应用，如力学中的功、能量、动量等概念都与积分有关。\n",
    "- **经济学应用**：在经济学中，积分常用于计算成本、收益、利润等经济指标的累积效果。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8a6890cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<>:22: SyntaxWarning: invalid escape sequence '\\p'\n",
      "<>:22: SyntaxWarning: invalid escape sequence '\\p'\n",
      "C:\\Users\\15487\\AppData\\Local\\Temp\\ipykernel_32948\\2316201734.py:22: SyntaxWarning: invalid escape sequence '\\p'\n",
      "  plt.title('First Derivative $f^{\\prime}(x)$')\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extremum points (x, f(x)):\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import symbols, sin, exp, diff, lambdify\n",
    "x = symbols('x')\n",
    "f = sin(x) * exp(x)\n",
    "f_prime = diff(f, x)\n",
    "f_lambda = lambdify(x, f, 'numpy')\n",
    "f_prime_lambda = lambdify(x, f_prime, 'numpy')\n",
    "x_values = np.linspace(-2 * np.pi, 2 * np.pi, 1000)\n",
    "f_values = f_lambda(x_values)\n",
    "f_prime_values = f_prime_lambda(x_values)\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(x_values, f_values, label=r'$f(x) = \\sin(x) \\cdot e^x$')\n",
    "plt.title('Function $f(x)$')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.plot(x_values, f_prime_values, label=r'$f^{\\prime}(x)$', color='orange')\n",
    "plt.title('First Derivative $f^{\\prime}(x)$')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel(r'$f^{\\prime}(x)$')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "extremum_points = np.where(np.isclose(f_prime_values, 0))[0]\n",
    "extremum_x_values = x_values[extremum_points]\n",
    "extremum_y_values = f_values[extremum_points]\n",
    "print(\"Extremum points (x, f(x)):\")\n",
    "for x_val, y_val in zip(extremum_x_values, extremum_y_values):\n",
    "    print(f\"({x_val:.2f}, {y_val:.2f})\")\n",
    "# 验证极值点是否为一阶导数的零点\n",
    "for x_val in extremum_x_values:\n",
    "    print(f\"f'(x={x_val:.2f}) = {f_prime_lambda(x_val):.6e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ca89b2c",
   "metadata": {},
   "source": [
    "# 多元函数极限与连续（54-127）（下册）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "228ff6d2",
   "metadata": {},
   "source": [
    "### 多元函数极限与连续知识点\n",
    "\n",
    "#### 一、多元函数极限\n",
    "\n",
    "**定义**：\n",
    "\n",
    "设函数 $f(x, y)$ 在点 $P_0(x_0, y_0)$ 的某一去心邻域内有定义，如果存在常数 $A$，对于任意给定的正数 $\\epsilon$，总存在正数 $\\delta$，使得当点 $P(x, y)$ 满足 $0 < \\sqrt{(x - x_0)^2 + (y - y_0)^2} < \\delta$ 时，有 $|f(x, y) - A| < \\epsilon$ 成立，那么就称常数 $A$ 为函数 $f(x, y)$ 当 $(x, y) \\to (x_0, y_0)$ 时的极限，记作 $\\lim_{(x, y) \\to (x_0, y_0)} f(x, y) = A$。\n",
    "\n",
    "**性质**：\n",
    "\n",
    "1. **唯一性**：若极限存在，则必唯一。\n",
    "2. **局部有界性**：若 $\\lim_{(x, y) \\to (x_0, y_0)} f(x, y) = A$，则存在点 $P_0$ 的某个去心邻域，使得函数 $f(x, y)$ 在该邻域内有界。\n",
    "3. **局部保号性**：若 $\\lim_{(x, y) \\to (x_0, y_0)} f(x, y) = A$，且 $A > 0$（或 $A < 0$），则存在点 $P_0$ 的某个去心邻域，使得在该邻域内 $f(x, y) > 0$（或 $f(x, y) < 0$）。\n",
    "\n",
    "**求法**：\n",
    "\n",
    "1. **直接代入法**：若函数在点 $(x_0, y_0)$ 处连续，则可直接代入求极限。\n",
    "2. **夹逼定理**：利用不等式关系，通过夹逼求出极限。\n",
    "3. **方向导数法**：考虑函数沿不同方向趋近于 $(x_0, y_0)$ 时的极限值，若所有方向上的极限值都相等，则此极限值即为所求。\n",
    "\n",
    "#### 二、多元函数连续性\n",
    "\n",
    "**定义**：\n",
    "\n",
    "设函数 $f(x, y)$ 在点 $P_0(x_0, y_0)$ 的定义域内，若 $\\lim_{(x, y) \\to (x_0, y_0)} f(x, y) = f(x_0, y_0)$，则称函数 $f(x, y)$ 在点 $P_0(x_0, y_0)$ 处连续。\n",
    "\n",
    "**性质**：\n",
    "\n",
    "1. **有界性**：若函数在某闭区域 $D$ 上连续，则该函数在 $D$ 上有界。\n",
    "2. **最值定理**：若函数在某闭区域 $D$ 上连续，则该函数在 $D$ 上必能取得最大值和最小值。\n",
    "3. **介值定理**：若函数在某闭区间 $[a, b]$ 上的两个端点处取值 $f(a)$ 和 $f(b)$，且 $u$ 是介于 $f(a)$ 和 $f(b)$ 之间的任意实数，则至少存在一点 $c \\in (a, b)$，使得 $f(c) = u$。\n",
    "\n",
    "**判断方法**：\n",
    "\n",
    "1. **直接验证法**：根据连续性的定义直接验证。\n",
    "2. **利用已知连续函数**：若函数 $f(x, y)$ 可表示为已知连续函数的和、差、积、商（分母不为零）等形式，则 $f(x, y)$ 也连续。\n",
    "3. **复合函数连续性**：若函数 $u = g(x, y)$ 在点 $(x_0, y_0)$ 处连续，且函数 $y = f(u)$ 在点 $u_0 = g(x_0, y_0)$ 处连续，则复合函数 $y = f[g(x, y)]$ 在点 $(x_0, y_0)$ 处也连续。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "e3a44c6c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "高斯-勒让德积分结果: 7.86466146359932\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, Lambda, sqrt\n",
    "\n",
    "# 定义符号变量\n",
    "x = symbols('x')\n",
    "\n",
    "# 高斯-勒让德节点和权重（这里假设是预先计算好的）\n",
    "xi = [-0.97391, -0.86506, -0.67941, -0.43340, -0.14887, 0.14887, 0.43340, 0.67941, 0.86506, 0.97391]\n",
    "wi = [0.066671, 0.14945, 0.21909, 0.26927, 0.29552, 0.29552, 0.26927, 0.21909, 0.14945, 0.066671]\n",
    "\n",
    "# 定义被积函数\n",
    "f = Lambda(x, sqrt(16 + 6*x - x**2))\n",
    "\n",
    "# 初始化积分和\n",
    "gauss_sum = 0\n",
    "\n",
    "# 计算高斯-勒让德积分\n",
    "for i in range(len(xi)):\n",
    "    gauss_sum += wi[i] * f(xi[i])\n",
    "\n",
    "# 输出结果\n",
    "print(\"高斯-勒让德积分结果:\", gauss_sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba24e242",
   "metadata": {},
   "source": [
    "# 偏导数与全微分（135-185）（下册）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5849039",
   "metadata": {},
   "source": [
    "### 偏导数与全微分知识点\n",
    "\n",
    "#### 一、偏导数\n",
    "\n",
    "**定义**：\n",
    "\n",
    "设二元函数 $z = f(x, y)$ 在点 $(x_0, y_0)$ 的某邻域内有定义，若极限\n",
    "\n",
    "$\\lim_{{\\Delta x \\to 0}} \\frac{f(x_0 + \\Delta x, y_0) - f(x_0, y_0)}{\\Delta x}$\n",
    "\n",
    "存在，则称此极限值为函数 $z = f(x, y)$ 在点 $(x_0, y_0)$ 处关于 $x$ 的偏导数，记作 $\\frac{\\partial z}{\\partial x} \\bigg|_{(x_0, y_0)}$ 或 $f_x(x_0, y_0)$。\n",
    "\n",
    "类似地，可以定义函数 $z = f(x, y)$ 在点 $(x_0, y_0)$ 处关于 $y$ 的偏导数。\n",
    "\n",
    "**几何意义**：\n",
    "\n",
    "偏导数表示函数在固定面上一点沿某一坐标轴方向的切线斜率。例如，$\\frac{\\partial z}{\\partial x} \\bigg|_{(x_0, y_0)}$ 表示函数 $z = f(x, y)$ 在点 $(x_0, y_0)$ 处沿 $x$ 轴方向的切线斜率。\n",
    "\n",
    "**性质**：\n",
    "\n",
    "1. 若函数 $z = f(x, y)$ 在某点 $(x_0, y_0)$ 处可导，则该函数在该点处关于 $x$ 和 $y$ 的偏导数必定存在。\n",
    "2. 偏导数存在不一定意味着函数在该点连续。\n",
    "\n",
    "#### 二、全微分\n",
    "\n",
    "**定义**：\n",
    "\n",
    "设二元函数 $z = f(x, y)$ 在点 $(x_0, y_0)$ 的某邻域内有定义，若函数的全增量 $\\Delta z = f(x_0 + \\Delta x, y_0 + \\Delta y) - f(x_0, y_0)$ 可以表示为 $A\\Delta x + B\\Delta y + o(\\rho)$ 的形式，其中 $\\rho = \\sqrt{(\\Delta x)^2 + (\\Delta y)^2}$，且 $o(\\rho)$ 是 $\\rho$ 的高阶无穷小，则称函数 $z = f(x, y)$ 在点 $(x_0, y_0)$ 处可微。此时，$A\\Delta x + B\\Delta y$ 称为函数在点 $(x_0, y_0)$ 处的全微分，记作 $dz \\bigg|_{(x_0, y_0)} = Adx + Bdy$。\n",
    "\n",
    "**几何意义**：\n",
    "\n",
    "全微分表示函数在某一点处沿任意方向的变化率。在二元函数中，全微分可以看作是在该点处切平面上的一个微小变化量。\n",
    "\n",
    "**性质**：\n",
    "\n",
    "1. 若函数在某点可微，则该函数在该点连续。\n",
    "2. 可微的充分条件是函数在该点的一阶偏导数存在且连续。\n",
    "3. 全微分与偏导数的关系：若函数 $z = f(x, y)$ 在点 $(x, y)$ 处可微，则 $A = f_x(x, y)$，$B = f_y(x, y)$。\n",
    "\n",
    "**可微性的验证**：\n",
    "\n",
    "验证多元函数的可微性，只需验证下式是否成立：\n",
    "\n",
    "$\\lim_{{\\rho \\to 0^+}} \\frac{\\Delta z - f_x\\Delta x - f_y\\Delta y}{\\rho} = 0$\n",
    "\n",
    "若上式成立，则函数在该点可微。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "fad691f5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df/dx: -x*sin(sqrt(x**2 + y**2))/sqrt(x**2 + y**2)\n",
      "df/dy: -y*sin(sqrt(x**2 + y**2))/sqrt(x**2 + y**2)\n",
      "d^2f/dxdy: x*y*(-cos(sqrt(x**2 + y**2))/(x**2 + y**2) + sin(sqrt(x**2 + y**2))/(x**2 + y**2)**(3/2))\n",
      "df/dx at (1, 2): -0.351844907875699\n",
      "df/dy at (1, 2): -0.703689815751398\n",
      "d^2f/dxdy at (1, 2): 0.38764711373314625\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, Lambda, cos, sqrt\n",
    "x, y = symbols('x y')\n",
    "f = Lambda((x, y), cos(sqrt(x**2 + y**2)))\n",
    "df_dx = f(x, y).diff(x)\n",
    "df_dy = f(x, y).diff(y)\n",
    "df_dxdy = f(x, y).diff(x, y)\n",
    "print(\"df/dx:\", df_dx)\n",
    "print(\"df/dy:\", df_dy)\n",
    "print(\"d^2f/dxdy:\", df_dxdy)\n",
    "df_dx_num = float(df_dx.subs(x, 1).subs(y, 2))\n",
    "df_dy_num = float(df_dy.subs(x, 1).subs(y, 2))\n",
    "df_dxdy_num = float(df_dxdy.subs(x, 1).subs(y, 2))\n",
    "print(\"df/dx at (1, 2):\", df_dx_num)\n",
    "print(\"df/dy at (1, 2):\", df_dy_num)\n",
    "print(\"d^2f/dxdy at (1, 2):\", df_dxdy_num)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59560293",
   "metadata": {},
   "source": [
    "# 多元函数积分(188-294)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd3fe983",
   "metadata": {},
   "source": [
    "\n",
    "# 多元函数积分知识点\n",
    "\n",
    "## 一、多元函数积分的概念\n",
    "\n",
    "### 1. 二重积分\n",
    "\n",
    "**定义**：设函数$f(x, y)$在平面区域$D$上有定义，将$D$任意划分成$n$个小区域$\\Delta\\sigma_1, \\Delta\\sigma_2, \\ldots, \\Delta\\sigma_n$，记$\\Delta\\sigma_i$的面积为$\\Delta S_i$，在每个小区域上任取一点$(x_i, y_i)$，作乘积$f(x_i, y_i)\\Delta S_i$（$i=1,2,\\ldots,n$），并求和$\\sum_{i=1}^{n}f(x_i, y_i)\\Delta S_i$，若当各小区域的直径中的最大值趋于0时，这个和式的极限存在，则称此极限为函数$f(x, y)$在区域$D$上的二重积分，记为$\\iint_{D}f(x, y)dxdy$。\n",
    "\n",
    "### 2. 三重积分\n",
    "\n",
    "**定义**：设函数$f(x, y, z)$在空间区域$G$上有定义，将$G$任意划分成$n$个小区域$\\Delta V_1, \\Delta V_2, \\ldots, \\Delta V_n$，记$\\Delta V_i$的体积为$\\Delta V_i$，在每个小区域上任取一点$(x_i, y_i, z_i)$，作乘积$f(x_i, y_i, z_i)\\Delta V_i$（$i=1,2,\\ldots,n$），并求和$\\sum_{i=1}^{n}f(x_i, y_i, z_i)\\Delta V_i$，若当各小区域的直径中的最大值趋于0时，这个和式的极限存在，则称此极限为函数$f(x, y, z)$在区域$G$上的三重积分，记为$\\iiint_{G}f(x, y, z)dxdydz$。\n",
    "\n",
    "## 二、多元函数积分的计算\n",
    "\n",
    "### 1. 二重积分的计算\n",
    "\n",
    "- **直角坐标系下的计算**：通过选择合适的积分顺序（先对$x$后对$y$，或先对$y$后对$x$），将二重积分转化为累次积分进行计算。\n",
    "- **极坐标系下的计算**：在极坐标系下，二重积分可以表示为$\\int_{\\theta_1}^{\\theta_2}d\\theta\\int_{r_1(\\theta)}^{r_2(\\theta)}f(r\\cos\\theta, r\\sin\\theta)rdr$，其中$r$和$\\theta$分别为极径和极角。\n",
    "\n",
    "### 2. 三重积分的计算\n",
    "\n",
    "- **直角坐标系下的计算**：根据积分区域的形状和函数的特点，选择合适的积分顺序（如先对$z$后对$x,y$，或先对$x$后对$y,z$等），将三重积分转化为累次积分进行计算。\n",
    "- **柱面坐标系下的计算**：在柱面坐标系下，三重积分可以表示为$\\int_{\\theta_1}^{\\theta_2}d\\theta\\int_{z_1(\\theta)}^{z_2(\\theta)}dz\\int_{r_1(z,\\theta)}^{r_2(z,\\theta)}f(r\\cos\\theta, r\\sin\\theta, z)rdr$。\n",
    "- **球面坐标系下的计算**：在球面坐标系下，三重积分可以表示为$\\int_{\\varphi_1}^{\\varphi_2}d\\varphi\\int_{\\theta_1}^{\\theta_2}\\sin\\varphi d\\theta\\int_{r_1(\\varphi,\\theta)}^{r_2(\\varphi,\\theta)}f(\\rho\\sin\\varphi\\cos\\theta, \\rho\\sin\\varphi\\sin\\theta, \\rho\\cos\\varphi)\\rho^2d\\rho$，其中$\\rho$、$\\varphi$和$\\theta$分别为径向距离、极角和方位角。\n",
    "\n",
    "## 三、多元函数积分的性质与定理\n",
    "\n",
    "- **线性性质**：积分运算满足线性运算规则，即对于任意常数$k$和$l$，以及任意两个可积函数$f(x, y)$和$g(x, y)$，有$\\iint_{D}[kf(x, y)+lg(x, y)]dxdy=k\\iint_{D}f(x, y)dxdy+l\\iint_{D}g(x, y)dxdy$。\n",
    "- **可加性**：若区域$D$可划分为两个互不重叠的子区域$D_1$和$D_2$，则$\\iint_{D}f(x, y)dxdy=\\iint_{D_1}f(x, y)dxdy+\\iint_{D_2}f(x, y)dxdy$。\n",
    "- **积分中值定理**：若函数$f(x, y)$在闭区域$D$上连续，则存在点$(x_0, y_0)\\in D$，使得$\\iint_{D}f(x, y)dxdy=f(x_0, y_0)S$，其中$S$为区域$D$的面积。\n",
    "- **积分与路径无关**：对于某些特殊的二元函数积分，其值与积分路径无关，只与积分区域的边界和端点有关。这通常与向量场中的线积分和势函数有关。\n",
    "\n",
    "## 四、应用实例\n",
    "\n",
    "多元函数积分在物理学、工程学、经济学等领域有广泛应用。例如，在物理学中，二重积分可以用于计算物体的质量、重心、转动惯量等；三重积分可以用于计算物体的体积、质心、静矩等。在工程学中，多元函数积分可以用于计算结构的应力、应变、位移等。在经济学中，多元函数积分可以用于计算经济指标、预测市场趋势等。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "e1accbea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "x = np.linspace(-2*np.pi, 2*np.pi, 100)\n",
    "y = np.linspace(-2*np.pi, 2*np.pi, 100)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = np.sin(np.sqrt(X**2 + Y**2))\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "surf = ax.plot_surface(X, Y, Z, cmap='viridis')\n",
    "fig.colorbar(surf)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fdfcc79",
   "metadata": {},
   "source": [
    "### 三、级数"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "570a31ba",
   "metadata": {},
   "source": [
    "# 数项级数（251-327）（下册）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6256772c",
   "metadata": {},
   "source": [
    "# 数项级数知识点\n",
    "## 1. 定义与分类\n",
    "- **定义**：数项级数是由一系列实数（或复数）按照一定顺序排列而成的序列的和，表示为 $\\sum_{n=1}^{\\infty} a_n$ 或 $\\sum a_n$。\n",
    "- **分类**：\n",
    "  - 有限级数：项数有限的级数。\n",
    "  - 无穷级数：项数无限的级数。\n",
    "  - 正项级数：所有项均为非负的级数。\n",
    "  - 交错级数：正负项交替出现的级数。\n",
    "  - 一般级数：项的正负无特定规律的级数。\n",
    "## 2. 收敛与发散\n",
    "- **收敛**：如果级数 $\\sum a_n$ 的部分和序列有界且存在极限 $S$，则称级数收敛于 $S$。\n",
    "- **发散**：如果级数 $\\sum a_n$ 的部分和序列无界或不存在极限，则称级数发散。\n",
    "## 3. 收敛判别法\n",
    "- **比较判别法**：通过比较级数的项与已知收敛或发散的级数的项来判断。\n",
    "- **比值判别法**（达朗贝尔）：利用相邻两项的比值的极限判断。\n",
    "- **根值判别法**（柯西）：利用项的绝对值的n次方根的极限判断。\n",
    "- **积分判别法**：通过比较级数的项与某个函数的积分判断。\n",
    "- **交错级数的莱布尼茨判别法**：满足条件则交错级数收敛。\n",
    "## 4. 级数的性质与运算\n",
    "- **线性运算**：加法、减法、数乘满足分配律和结合律。\n",
    "- **乘法**：两个级数的乘积可通过柯西乘积公式展开。\n",
    "- **重排**：发散级数通过改变排列顺序可能得到不同极限（黎曼重排）。\n",
    "- **裂项**：将复杂项分解为简单项之差，利用裂项相消法求和。\n",
    "## 5. 重要的级数求和公式与例子\n",
    "- **等差数列**：$\\sum_{k=1}^{n} k = \\frac{n(n+1)}{2}$\n",
    "- **等比数列**：$\\sum_{k=0}^{n} ar^k = \\frac{a(1-r^{n+1})}{1-r}$（$r \\neq 1$）\n",
    "- **调和级数**：$\\sum_{n=1}^{\\infty} \\frac{1}{n}$ 发散。\n",
    "- **p-级数**：$\\sum_{n=1}^{\\infty} \\frac{1}{n^p}$，$p > 1$ 时收敛，$p \\leq 1$ 时发散。\n",
    "- **幂级数**：形如 $\\sum_{n=0}^{\\infty} a_n x^n$ 的级数，在 $x$ 的某些范围内可能收敛。\n",
    "## 6. 应用\n",
    "- **微积分**：通过级数表示函数，求解极限、导数、积分等。\n",
    "- **物理学**：求解物理问题的近似解，表示物理量的级数展开。\n",
    "- **工程学**：信号处理、控制系统设计等领域的近似计算。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "043281d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3049/1024\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, Lambda, summation, limit, oo\n",
    "\n",
    "n = symbols('n')\n",
    "f = Lambda(n, (2*n - 1) / 2**n)\n",
    "partial_sum = summation(f(n), (n, 1, 10))  \n",
    "print(partial_sum)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "972c7be5",
   "metadata": {},
   "source": [
    "# 函数项级数(299-330)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a56746a",
   "metadata": {},
   "source": [
    "# 函数项级数知识点\n",
    "\n",
    "## 定义与基本概念\n",
    "\n",
    "**函数项级数**：设$f_n(x)$（$n=1,2,3,\\ldots$）是定义在某一区间$I$上的函数列，则表达式\n",
    "\n",
    "$$S(x) = \\sum_{n=1}^{\\infty} f_n(x) = f_1(x) + f_2(x) + f_3(x) + \\cdots$$\n",
    "\n",
    "称为定义在区间$I$上的**函数项级数**。\n",
    "\n",
    "**部分和**：对于任意正整数$k$，称\n",
    "\n",
    "$$S_k(x) = \\sum_{n=1}^{k} f_n(x)$$\n",
    "\n",
    "为级数$S(x)$的**部分和**。\n",
    "\n",
    "**收敛与发散**：若存在函数$S(x)$，使得对于任意$x_0 \\in I$，当$k \\to \\infty$时，$S_k(x_0) \\to S(x_0)$，则称级数$S(x)$在点$x_0$收敛，$S(x_0)$为其和；若不存在这样的函数$S(x)$，则称级数在点$x_0$发散。\n",
    "\n",
    "**收敛域**：所有使级数收敛的$x$的集合称为级数的**收敛域**。\n",
    "\n",
    "## 收敛判别法\n",
    "\n",
    "### 魏尔斯特拉斯判别法（M-判别法）\n",
    "\n",
    "若存在正项数列$M_n$，使得对于所有$x \\in I$，有$|f_n(x)| \\leq M_n$，且级数$\\sum_{n=1}^{\\infty} M_n$收敛，则级数$\\sum_{n=1}^{\\infty} f_n(x)$在区间$I$上一致收敛。\n",
    "\n",
    "### 阿贝尔判别法与狄利克雷判别法\n",
    "\n",
    "- **阿贝尔判别法**：若$\\{f_n(x)\\}$单调，且级数$\\sum_{n=1}^{\\infty} M_n$（其中$M_n = \\sup_{x \\in I} |g_n(x)|$，$g_n(x)$为$f_n(x)$的某种变换或相关函数）收敛，则级数$\\sum_{n=1}^{\\infty} f_n(x)g_n(x)$在区间$I$上一致收敛。\n",
    "- **狄利克雷判别法**：若$\\{f_n(x)\\}$单调递减趋于0，且对于任意正整数$N$和任意$x \\in I$，级数$\\sum_{n=1}^{N} |g_{n+1}(x) - g_n(x)|$有界，则级数$\\sum_{n=1}^{\\infty} f_n(x)g_n(x)$在区间$I$上一致收敛。\n",
    "\n",
    "## 性质与定理\n",
    "\n",
    "- **和函数的连续性**：若函数项级数在区间$I$上一致收敛，则其和函数$S(x)$在$I$上连续。\n",
    "- **和函数的可积性**：若函数项级数在闭区间$[a,b]$上一致收敛，且每一项$f_n(x)$都在$[a,b]$上可积，则其和函数$S(x)$也在$[a,b]$上可积，且\n",
    "\n",
    "$$\\int_a^b S(x) \\, dx = \\int_a^b \\sum_{n=1}^{\\infty} f_n(x) \\, dx = \\sum_{n=1}^{\\infty} \\int_a^b f_n(x) \\, dx$$\n",
    "\n",
    "- **和函数的可导性**：若函数项级数在区间$I$上每一项都可导，且其导函数级数在$I$上一致收敛，则其和函数$S(x)$在$I$上也可导，且\n",
    "\n",
    "$$S'(x) = \\left(\\sum_{n=1}^{\\infty} f_n(x)\\right)' = \\sum_{n=1}^{\\infty} f_n'(x)$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "02b65890",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "前1000项的部分和为: 0.915965094178718\n",
      "通过数学分析得出的真实和为: 2.193245422464302\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, sin, summation, oo\n",
    "from math import pi \n",
    "x = symbols('x')\n",
    "n = symbols('n')\n",
    "term = sin(n*x) / n**2\n",
    "partial_sum = lambda k: summation(term.subs(x, pi/2), (n, 1, k))\n",
    "approx_sum = partial_sum(1000)\n",
    "print(f\"前1000项的部分和为: {approx_sum}\")\n",
    "true_sum = (2 * pi**2) / 9\n",
    "print(f\"通过数学分析得出的真实和为: {true_sum}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc380743",
   "metadata": {},
   "source": [
    "# 幂级数（272-290）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd370fa0",
   "metadata": {},
   "source": [
    "\n",
    "# 幂级数知识点\n",
    "\n",
    "## 定义与基本概念\n",
    "\n",
    "**幂级数**：形如\n",
    "\n",
    "$$ \\sum_{n=0}^{\\infty} a_n (x-c)^n = a_0 + a_1(x-c) + a_2(x-c)^2 + \\cdots $$\n",
    "\n",
    "的函数项级数称为**幂级数**，其中$a_n$（$n=0,1,2,\\ldots$）是常数，$c$是常数项，$x$是变量。\n",
    "\n",
    "**收敛点**：若存在某个$x_0$，使得级数$\\sum_{n=0}^{\\infty} a_n (x_0-c)^n$收敛，则称$x_0$为幂级数的**收敛点**。\n",
    "\n",
    "**发散点**：若不存在$x_0$使得级数收敛，则称该点为幂级数的**发散点**。\n",
    "\n",
    "**收敛域**：所有收敛点的集合称为幂级数的**收敛域**。\n",
    "\n",
    "**收敛半径**：设幂级数$\\sum_{n=0}^{\\infty} a_n (x-c)^n$的收敛域为$(c-R, c+R)$（$R>0$）或$[c-R, c+R]$（$R>0$）或$c$（当级数仅在一点收敛时），则称$R$为该幂级数的**收敛半径**。\n",
    "\n",
    "## 收敛判别法\n",
    "\n",
    "### 比值判别法（达朗贝尔判别法）\n",
    "\n",
    "设幂级数$\\sum_{n=0}^{\\infty} a_n (x-c)^n$的相邻两项之比的极限为\n",
    "\n",
    "$$\\rho = \\lim_{{n \\to \\infty}} \\left| \\frac{a_{{n+1}}}{a_n} \\right|$$\n",
    "\n",
    "若$\\rho$存在，则\n",
    "\n",
    "- 当$\\rho < 1$时，级数在$(c-1/\\rho, c+1/\\rho)$内收敛；\n",
    "- 当$\\rho > 1$时，级数在$(c-1/\\rho, c+1/\\rho)$外发散；\n",
    "- 当$\\rho = 1$时，判别法失效。\n",
    "\n",
    "### 根值判别法（柯西判别法）\n",
    "\n",
    "设幂级数$\\sum_{n=0}^{\\infty} a_n (x-c)^n$的项绝对值的$n$次方根的极限为\n",
    "\n",
    "$$\\sigma = \\lim_{{n \\to \\infty}} \\sqrt[n]{|a_n|}$$\n",
    "\n",
    "若$\\sigma$存在，则\n",
    "\n",
    "- 当$\\sigma < 1$时，级数在$(c-\\frac{1}{\\sigma}, c+\\frac{1}{\\sigma})$内收敛；\n",
    "- 当$\\sigma > 1$时，级数在$(c-\\frac{1}{\\sigma}, c+\\frac{1}{\\sigma})$外发散；\n",
    "- 当$\\sigma = 1$时，判别法失效。\n",
    "\n",
    "## 性质与定理\n",
    "\n",
    "- **唯一性定理**：一个函数在其收敛域内不能表示为两个不同的幂级数之和。\n",
    "- **逐项求导与积分**：幂级数在其收敛域内可以逐项求导与积分，且结果仍为幂级数。\n",
    "- **阿贝尔定理**：若幂级数在点$x_0$（$x_0 \\neq c$）处收敛，则对于所有满足$|x-c| < |x_0-c|$的$x$，级数也收敛；若级数在点$x_1$（$x_1 \\neq c$）处发散，则对于所有满足$|x-c| > |x_1-c|$的$x$，级数也发散。\n",
    "- **性质推广**：若幂级数在某区间$[a, b]$（$a < c < b$）内收敛，则对于任意满足$a < x < b$的$x$，级数都收敛，且收敛域至少为$(a, b)$的一个子集。\n",
    "\n",
    "## 应用实例\n",
    "\n",
    "幂级数在函数逼近、微分方程求解、复变函数论等领域有广泛应用。例如，利用幂级数可以求解一些初值问题的解，如指数函数、三角函数、对数函数等都可以通过幂级数展开来表示。此外，幂级数还可以用于近似计算复杂函数的值，以及分析函数的性质等。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "f4e1b8a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "前1000项的部分和为: 0.870419751367104\n",
      "通过数学分析得出的真实和为: 0.463647609000806\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, summation, limit, oo, atan\n",
    "x = symbols('x')\n",
    "n = symbols('n')\n",
    "term = (-1)**n / (2*n + 1) * x**n\n",
    "partial_sum = lambda k: summation(term, (n, 0, k))\n",
    "approx_sum = partial_sum(1000).subs(x, 1/2)\n",
    "print(f\"前1000项的部分和为: {approx_sum}\")\n",
    "true_sum = atan(1/2)\n",
    "print(f\"通过数学分析得出的真实和为: {true_sum}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bba9461",
   "metadata": {},
   "source": [
    "### 四、微分方程"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25a8ca98",
   "metadata": {},
   "source": [
    "# 常微分方程（297-360）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c998019e",
   "metadata": {},
   "source": [
    "# 常微分方程（ODE）知识点\n",
    "## 1. 常微分方程的基本概念\n",
    "- **定义**：常微分方程是描述一个或多个未知函数及其导数（或微分）与自变量之间关系的方程。若方程中仅含一个自变量，则称为一元常微分方程；若方程中含多个自变量，则称为偏微分方程（但本文重点讨论常微分方程）。\n",
    "- **阶数**：根据方程中出现的最高阶导数的次数划分，如一阶常微分方程、二阶常微分方程等。\n",
    "- **线性与非线性**：若方程中未知函数及其各阶导数的次数均为1，且方程中不含未知函数的复合函数或乘积，则称为线性常微分方程；否则，称为非线性常微分方程。\n",
    "## 2. 初值问题与边值问题\n",
    "- **初值问题**：给定一个或多个初始条件（即某一点或几个点上的函数值或导数值），求解常微分方程的问题。\n",
    "- **边值问题**：在求解区域的边界上给定条件，求解常微分方程的问题。在常微分方程中，边值问题较少见，更多出现在偏微分方程中。但在某些特殊情况下，如积分方程或某些类型的变换后，常微分方程也可能出现边值问题。\n",
    "## 3. 求解方法\n",
    "- **分离变量法**：适用于一阶齐次线性或可化为齐次的非线性常微分方程。\n",
    "- **积分因子法**：用于求解一阶非齐次线性常微分方程。\n",
    "- **常数变易法**：从一阶线性齐次方程的通解出发，通过常数变易得到非齐次方程的通解。\n",
    "- **降阶法**：对于高阶常微分方程，可通过构造新的变量将其降为一阶方程组来求解。\n",
    "- **幂级数法**：用于求解某些类型的非线性常微分方程，特别是当方程可表示为幂级数形式时。\n",
    "- **拉普拉斯变换法**：适用于某些类型的积分方程或具有特定边界条件的常微分方程。\n",
    "- **数值方法**：如欧拉法、龙格-库塔法等，用于求解不能或难以找到精确解的常微分方程。\n",
    "## 4. 稳定性与奇点\n",
    "- **稳定性**：在数值求解或分析解的长期行为时，考虑解是否对初始条件的微小变化敏感。\n",
    "- **奇点**：使方程无定义的点，或在该点上解的行为发生显著变化的点。奇点可能是方程的解，也可能是解的间断点或不可达点。\n",
    "## 5. 应用领域\n",
    "- **物理学**：如力学、电磁学、热力学等中的运动规律描述。\n",
    "- **工程学**：如电路分析、控制系统、信号处理等。\n",
    "- **经济学**：如人口增长模型、资本积累模型等。\n",
    "- **生物学**：如传染病模型、生态系统模型等。\n",
    "- **化学**：如化学反应速率模型等。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a6420f07",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "例题 1: 一阶线性微分方程 dy/dx + 2y = x 的解为：\n",
      "Eq(y(x), C1*exp(-2*x) + x/2 - 1/4)\n",
      "\n",
      "例题 2: 二阶常系数齐次微分方程 y'' - 3y' + 2y = 0 的解为：\n",
      "Eq(y(x), (C1 + C2*exp(x))*exp(x))\n"
     ]
    }
   ],
   "source": [
    "import sympy as sp\n",
    "\n",
    "# 定义符号\n",
    "x = sp.symbols('x')\n",
    "y = sp.Function('y')(x)  \n",
    "y_prime = y.diff(x)      \n",
    "y_double_prime = y.diff(x, 2)  \n",
    "# 例题 1: 一阶线性微分方程 dy/dx + 2y = x\n",
    "eq1 = sp.Eq(y_prime + 2*y, x)\n",
    "solution1 = sp.dsolve(eq1, y)\n",
    "# 例题 2: 二阶常系数齐次微分方程 y'' - 3y' + 2y = 0\n",
    "eq2 = sp.Eq(y_double_prime - 3*y_prime + 2*y, 0)\n",
    "solution2 = sp.dsolve(eq2, y)\n",
    "print(\"例题 1: 一阶线性微分方程 dy/dx + 2y = x 的解为：\")\n",
    "print(solution1)\n",
    "print(\"\\n例题 2: 二阶常系数齐次微分方程 y'' - 3y' + 2y = 0 的解为：\")\n",
    "print(solution2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b802c135",
   "metadata": {},
   "source": [
    "# 偏微分方程（微分方程拓展）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d80de61",
   "metadata": {},
   "source": [
    "\n",
    "# 偏微分方程（PDE）\n",
    "## 1. PDE的基本概念\n",
    "- **定义**：偏微分方程是描述多个自变量之间关系的微分方程，它包含未知函数的偏导数。\n",
    "- **分类**：\n",
    "  - **椭圆型PDE**：通常与稳态问题相关，如调和方程。\n",
    "  - **抛物型PDE**：通常与扩散或热传导等随时间演变的过程相关。\n",
    "  - **双曲型PDE**：通常与波动或传播现象相关，如声波或电磁波。\n",
    "## 2. 边界条件和初始条件\n",
    "- **边界条件**：描述了PDE在边界上的行为，可以是：\n",
    "  - **Dirichlet条件**：指定函数值。\n",
    "  - **Neumann条件**：指定函数梯度的法向分量。\n",
    "  - **Robin条件**：Dirichlet和Neumann条件的线性组合。\n",
    "- **初始条件**：对于时间相关的PDE，初始条件描述了系统在初始时刻的状态。\n",
    "## 3. 数值方法\n",
    "- **有限差分法**：将连续的空间和时间域离散化为网格，通过泰勒级数展开来近似偏导数，从而得到一组代数方程。\n",
    "- **有限元法**：将PDE的解域划分为有限数量的子域（元素），在每个元素上构建近似解，并通过变分原理或加权余量法得到一组代数方程。\n",
    "- **谱方法**：利用全局基函数（如三角函数）来展开未知函数，从而得到一组代数方程。这种方法特别适用于周期性问题。\n",
    "## 4. 解析解\n",
    "在极少数情况下，可以通过数学技巧（如分离变量法、特征函数法等）找到PDE的精确解。\n",
    "## 5. 稳定性、收敛性和误差分析\n",
    "- **稳定性**：数值方法在求解过程中不应导致解的发散。\n",
    "- **收敛性**：当网格尺寸趋于零时，数值解应趋近于精确解。\n",
    "- **误差分析**：量化数值解与精确解之间的差异，包括截断误差和舍入误差。\n",
    "## 6. 应用领域\n",
    "- **物理学**：如流体力学、电磁学、量子力学等。\n",
    "- **工程学**：如结构力学、热传导、声学等。\n",
    "- **金融学**：如期权定价、风险管理等。\n",
    "- **生物学**：如种群动力学、疾病传播等。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "58927318",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 19968 (\\N{CJK UNIFIED IDEOGRAPH-4E00}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 32500 (\\N{CJK UNIFIED IDEOGRAPH-7EF4}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 28909 (\\N{CJK UNIFIED IDEOGRAPH-70ED}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 26041 (\\N{CJK UNIFIED IDEOGRAPH-65B9}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 31243 (\\N{CJK UNIFIED IDEOGRAPH-7A0B}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 30340 (\\N{CJK UNIFIED IDEOGRAPH-7684}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 26377 (\\N{CJK UNIFIED IDEOGRAPH-6709}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 38480 (\\N{CJK UNIFIED IDEOGRAPH-9650}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 24046 (\\N{CJK UNIFIED IDEOGRAPH-5DEE}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 20998 (\\N{CJK UNIFIED IDEOGRAPH-5206}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n",
      "c:\\Users\\15487\\AppData\\Local\\Programs\\Python\\Python313\\Lib\\site-packages\\IPython\\core\\pylabtools.py:170: UserWarning: Glyph 35299 (\\N{CJK UNIFIED IDEOGRAPH-89E3}) missing from font(s) DejaVu Sans.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 参数\n",
    "L = 1.0  # 长度\n",
    "T = 0.5  # 时间\n",
    "alpha = 0.01  # 热扩散系数\n",
    "Nx = 50  # 空间网格点数\n",
    "Nt = 1000  # 时间步数\n",
    "dx = L / (Nx - 1)  # 空间步长\n",
    "dt = T / Nt  # 时间步长\n",
    "\n",
    "# 检查稳定性条件\n",
    "r = alpha * dt / dx**2\n",
    "if r > 0.5:\n",
    "    raise ValueError(\"时间步长太大，不满足稳定性条件\")\n",
    "\n",
    "# 初始化网格\n",
    "x = np.linspace(0, L, Nx)\n",
    "t = np.linspace(0, T, Nt + 1)\n",
    "u = np.zeros((Nx, Nt + 1))\n",
    "\n",
    "# 初始条件\n",
    "u[:, 0] = np.sin(np.pi * x / L)\n",
    "\n",
    "# 边界条件\n",
    "u[0, :] = 0\n",
    "u[-1, :] = 0\n",
    "\n",
    "# 时间迭代\n",
    "for n in range(Nt):\n",
    "    u_new = u.copy()\n",
    "    for i in range(1, Nx - 1):\n",
    "        u_new[i, n + 1] = u[i, n] + r * (u[i + 1, n] - 2 * u[i, n] + u[i - 1, n])\n",
    "    u = u_new\n",
    "\n",
    "# 绘图\n",
    "fig, ax = plt.subplots()\n",
    "X, T = np.meshgrid(x, t)\n",
    "CS = ax.contourf(X, T, u.T, levels=50, cmap='hot')\n",
    "fig.colorbar(CS, ax=ax)\n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('t')\n",
    "ax.set_title('一维热方程的有限差分解')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
